几乎导出匹配可扩图的一些度条件  

Study on degree constraints of general induced matching extendable graph

作　　者：杨田羽 王勤 YANG Tianyu;WANG Qin(College of Economics and Management,China Jiliang University,Hangzhou 310018,China;College of Sciences,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学经济与管理学院,浙江杭州310018 [2]中国计量大学理学院,浙江杭州310018

出　　处：《中国计量大学学报》2020年第1期125-128,共4页Journal of China University of Metrology

基　　金：国家自然科学基金项目(No.11171316)。

摘　　要：目的:研究图的完美匹配与几乎导出匹配可扩性的关系,研究无爪图是几乎导出匹配可扩图的度条件。方法:利用无爪图导出匹配的性质和几乎导出匹配可扩图的定义,以及n-可扩图度和条件的Plummer定理,推导证明度条件。结果:得到了几乎导出匹配可扩无爪图的度条件,研究了二部图的几乎导出匹配可扩性。结论:若图G是一个顶点数为2n-1的无爪图,如果对图G中任意不相邻的顶点u和v,有d(u)+d(v)≥2n+1,那么图G是几乎导出匹配可扩的,并证明了不存在几乎导出匹配可扩的二部图。Aims:To study the relationship between perfect matching and general induced matching extensibility of a graph,the degree conditions of claw-free graph to be induced matching extendable.Methods:Using the properties of the induced matching of claw-free graph and the definition of general induced matching extendable graph,together with Plummer s theory for the degree conditions of n-extendable graph,to deduce and prove the degree conditions.Results:The degree condition of general induced matching extendable claw-free graphs is obtained,and the general induced matching extensibility of bipartite graph is discussed.Conclusions:Suppose that G is a claw-free graph with 2n-1 vertices.If for each pair of nonadjacent vertices u and v in G,d(u)+d(v)≥2n+1,then G is general induced matching extendable.The general induced matching extendable bipartite graph does not exist.

关 键 词：计量 导出匹配 无爪图 二部图 完美匹配 

分 类 号：O157.5[理学—数学]